{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 高数笔记P152-156\n",
    "## 函数的极值与最大值最小值\n",
    "## 一、函数的极值及其求法\n",
    "在上节例4中我们看到，点x=1及x=2是函数\n",
    "\n",
    "$f(x)=2x^3-9x^2+12x-3$\n",
    "\n",
    "的单调区间的分界点．例如，在点x=1的左侧邻近，函数f(x）是单调增加的，在点x=1的右侧邻近，函数f(x）是单调减少的．因此，存在点x=1的一个去心邻域，对于这去心邻域内的任何点x,f(x)<f(1）均成立．类似地，关于点x=2，也存在着一个去心邻域，对于这去心邻域内的任何点x,f(x)>f(2）均成立（参看图3-6)．具有这种性质的点如x=1及x=2,在应用上有着重要的意义，值得我们对此作一般性的讨论．\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 定义 设函数f(x）在点x0的某邻域U(x0）内有定义，如果对于去心邻域U(x0）内的任一x，有$f(x)<f(xo)（或f(x)>f(xo))$,那么就称f(x0）是函数f(x）的一个极大值（或极小值）.\n",
    "函数的极大值与极小值统称为函数的极值，使函数取得极值的点称为极值点．例如，上节例4中的函数\n",
    "\n",
    "$f(x)=2x^3-9x^2+12x-3$\n",
    "\n",
    "有极大值f(1)=2和极小值f(2)=1，点x=1和x=2是函数f(x）的极值点．\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in c:\\users\\1\\anaconda3\\lib\\site-packages (1.26.4)\n",
      "Note: you may need to restart the kernel to use updated packages.\n",
      "Requirement already satisfied: matplotlib in c:\\users\\1\\anaconda3\\lib\\site-packages (3.8.4)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (1.2.0)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (0.11.0)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (4.51.0)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (1.4.4)\n",
      "Requirement already satisfied: numpy>=1.21 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (1.26.4)\n",
      "Requirement already satisfied: packaging>=20.0 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (23.2)\n",
      "Requirement already satisfied: pillow>=8 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (10.3.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (3.0.9)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in c:\\users\\1\\anaconda3\\lib\\site-packages (from matplotlib) (2.9.0.post0)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\1\\anaconda3\\lib\\site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install numpy\n",
    "%pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义函数\n",
    "def f(x):\n",
    "    return 2*x**3 - 9*x**2 + 12*x - 3\n",
    "\n",
    "# 生成x的值，从-1到4，间隔为1\n",
    "x_values = np.arange(-10, 15, 1)\n",
    "# 计算对应的y值\n",
    "y_values = f(x_values)\n",
    "\n",
    "# 创建图形\n",
    "plt.figure(figsize=(8, 6))\n",
    "\n",
    "# 绘制函数图像\n",
    "plt.plot(x_values, y_values, label='$f(x) = 2x^3 - 9x^2 + 12x - 3$')\n",
    "\n",
    "# 添加标题和标签\n",
    "plt.title('Plot of the Function $f(x) = 2x^3 - 9x^2 + 12x - 3$')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "\n",
    "# 显示网格\n",
    "plt.grid(True)\n",
    "\n",
    "# 显示图例\n",
    "plt.legend()\n",
    "\n",
    "# 显示图像\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "函数的极大值和极小值概念是局部性的．如果f(x0）是函数f(x）的一个极大值，那只是就xo附近的一个局部范围来说，f(xo）是f(x）的一个最大值；如果就f(x）的整个定义域来说，f(xo）不见得是最大值．关于极小值也类似\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义函数\n",
    "def f(x):\n",
    "    return x**4 - 8*x**3 + 18*x**2 - 12*x + 1\n",
    "\n",
    "# 生成x的值，从-1到5，间隔为0.01\n",
    "x_values = np.arange(-1, 5.01, 0.01)\n",
    "# 计算对应的y值\n",
    "y_values = f(x_values)\n",
    "\n",
    "# 计算导数来找到极值点（可选，用于验证）\n",
    "def df(x):\n",
    "    return 4*x**3 - 24*x**2 + 36*x - 12\n",
    "\n",
    "# 找到导数等于0的点（即极值点）\n",
    "critical_points = np.roots(np.array([4, -24, 36, -12]))\n",
    "critical_points = critical_points.real  # 只取实部，因为复数根在此上下文中没有意义\n",
    "\n",
    "# 过滤掉不在x_values范围内的极值点\n",
    "valid_critical_points = [cp for cp in critical_points if -1 <= cp <= 5]\n",
    "\n",
    "# 创建图形\n",
    "plt.figure(figsize=(8, 6))\n",
    "\n",
    "# 绘制函数图像\n",
    "plt.plot(x_values, y_values, label='$f(x) = x^4 - 8x^3 + 18x^2 - 12x + 1$')\n",
    "\n",
    "# 在极值点上绘制垂直线（可选，用于可视化）\n",
    "for cp in valid_critical_points:\n",
    "    plt.axvline(x=cp, color='red', linestyle='--', linewidth=0.5)\n",
    "\n",
    "# 添加标题和标签\n",
    "plt.title('Plot of the Function with Multiple Extrema')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "\n",
    "# 显示网格\n",
    "plt.grid(True)\n",
    "\n",
    "# 显示图例\n",
    "plt.legend()\n",
    "\n",
    "# 在极值点上方添加文本标签（可选）\n",
    "for i, cp in enumerate(valid_critical_points):\n",
    "    plt.text(cp, f(cp) + 1, f'Extrema {i+1}\\n({cp:.2f}, {f(cp):.2f})',\n",
    "             horizontalalignment='center', verticalalignment='bottom', fontsize=9)\n",
    "\n",
    "# 显示图像\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从图中还可看到，在函数取得极值处，曲线的切线是水平的．但曲线上有水平切线的地方，函数不一定取得极值．例如图中x=x3处，曲线上有水平切线，但f(x3）不是极值．\n",
    "\n",
    "由本章第一节费马引理可知，如果函数f(x）在x0处可导，且f(x）在xo处取得极值，那么f'(xo)=0．这就是可导函数取得极值的必要条件．现将此结论叙述成如下定理：\n",
    "\n",
    "### 定理1（必要条件） 设函数f(x）在x0处可导，且在x。处取得极值，则f'(x。)=0.\n",
    "定理1就是说：可导函数f(x）的极值点必定是它的驻点．但反过来，函数的驻点却不一定是极值点．例如，f(x)=x2的导数f'(x)=3x2,f'(0)=0，因此x=0是这可导函数的驻点，但x=0却不是这函数的极值点．所以，函数的驻点只是可能的极值点．此外，函数在它的导数不存在的点处也可能取得极值．例如，函数f(x)=1x1在点x=0处不可导，但函数在该点取得极小值．\n",
    "\n",
    "\n",
    "怎样判定函数在驻点或不可导的点处究竟是否取得极值？如果是的话，取得极大值还是极小值？下面给出两个判定极值的充分条件：\n",
    "\n",
    "### 定理2（第一充分条件） 设函数f(x）在xo处连续，且在xo的某去心邻域\n",
    "### (1）若$x \\in(x0-δ,xo）$时，f'(x)>0，而$x \\in(x0,xo+δ）$时，f'(x)<0，则f(x）在x0处取得极大值；\n",
    "### (2）若$x \\in(x0-δ,xo）$时，f'(x)<0，而$x \\in(x0,xo+δ）时，f'(x)>0，则f(x）在x0处取得极小值；\n",
    "### (3）若$x \\in U(x0,δ)$时f'(x）的符号保持不变，则f(x）在x0处没有极值证事实上，就情形（1）来说，根据函数单调性的判定法，函数f(x）在续的，故当x∈U(xo,δ）时，总有f(x)<f(xo)．所以，f(x0）是f(x）的一个极大值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义函数f(x)和f'(x)（这里假设f(x)在某个点x0处由正变为负，f'(x)在x0处穿过x轴）\n",
    "def f_b(x):\n",
    "    return -(x - 2)**2 + 4  # 示例函数，假设图(b)的f(x)为-(x-2)^2+4\n",
    "\n",
    "def f_prime_b(x):\n",
    "    return -2*(x - 2)  # 示例导数，假设图(b)的f'(x)为-2(x-2)\n",
    "\n",
    "# 绘制函数f(x)和f'(x)（类似图(a)的代码，但使用新的函数定义）\n",
    "x = np.linspace(-10, 10, 400)\n",
    "y = f_b(x)\n",
    "y_prime = f_prime_b(x)\n",
    "\n",
    "plt.plot(x, y, label='f(x)')\n",
    "plt.plot(x, y_prime, label='f\\'(x)', color='red')\n",
    "plt.legend()\n",
    "plt.title('图(b)：函数f(x)和其导数f\\'(x)的图像')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义函数f(x)和f'(x)（这里假设f(x)在某个点x0处由负变为正，f'(x)在整个区间内都是正的）\n",
    "def f_d(x):\n",
    "    return (x + 2)**2  # 示例函数，假设图(d)的f(x)为(x+2)^2\n",
    "\n",
    "def f_prime_d(x):\n",
    "    return 2*(x + 2)  # 示例导数，假设图(d)的f'(x)为2(x+2)\n",
    "\n",
    "# 绘制函数f(x)和f'(x)（类似图(a)的代码，但使用新的函数定义）\n",
    "x = np.linspace(-10, 10, 400)\n",
    "y = f_d(x)\n",
    "y_prime = f_prime_d(x)\n",
    "\n",
    "plt.plot(x, y, label='f(x)')\n",
    "plt.plot(x, y_prime, label='f\\'(x)', color='red')\n",
    "plt.legend()\n",
    "plt.title('图(d)：函数f(x)和其导数f\\'(x)的图像')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定理2也可简单地这样说：当x在xo的邻近渐增地经过x。时，如果f'(x）的符号由正变负，那么f(x）在xo处取得极大值；如果f'(x）的符号由负变正，那么f(x）在xo取得极小值；如果f'(x)的符号不改变，那么f(x)在x0处没有极值。\n",
    "\n",
    "根据上面的两个定理，如果函数f(x）在所讨论的区间内连续，除个别点外处处可导，那么就可以按下列步骤来求f(x）在该区间内的极值点和相应的极值：\n",
    "\n",
    "(1）求出导数f'(x);\n",
    "\n",
    "(2）求出f(x）的全部驻点与不可导点；\n",
    "\n",
    "(3）考察f'(x）的符号在每个驻点或不可导点的左、右邻近的情形，以确定该点是否为极值点；如果是极值点，进一步确定是极大值点还是极小值点；\n",
    "\n",
    "(4）求出各极值点的函数值，就得函数f(x）的全部极值．\n",
    "\n",
    "例1 求函数$f(x)=(x-4)\\sqrt[3](x+1)^2$的极值．\n",
    "解（1)f(x）在（-∞,+∞）内连续，除x=-1外处处可导，且\n",
    "\n",
    "$f'(x)=\\frac{5(x-1)}{3\\sqrt[3]{(x+1)^2}}$\n",
    "\n",
    "(2）令f'(x)=0，得驻点x=1,x=-1为f(x）的不可导点；\n",
    "\n",
    "(3）在（-∞,-1）内，f'(x)>0；在（-1,1）内，f'(x)<0．故不可导点x=-1是一个极大值点；又在（1,+∞）内，f'(x)>0，故驻点x=1是一个极小值点；\n",
    "\n",
    "(4）极大值为f(-1)=0，极小值为$f(1)=-3\\sqrt[3]{4}$\n",
    "当函数f(x）在驻点处的二阶导数存在且不为零时，也可以利用下述定理来判定f(x）在驻点处取得极大值还是极小值．\n",
    "\n",
    "### 定理3（第二充分条件） 设函数f(x）在x0处具有二阶导数且f'(x0)=0,f\"(x0)≠0，则只能判断与驻点．\n",
    "### (1）当f\"(xo)<0时，函数f(x）在x0处取得极大值；\n",
    "### (2）当f\"(xo)>0时，函数f(x）在xo处取得极小值．\n",
    "证在情形（1)，由于f\"(xo)<0，按二阶导数的定义有\n",
    "\n",
    "$f\"(x0)=lim \\frac{f'(x)-f'(xo)}{x-x0}<0.$\n",
    "\n",
    "根据函数极限的局部保号性，当x在x0的足够小的去心邻域内时，\n",
    "\n",
    "$\\frac{f'(x)-f'(xo)}{x-x0}<0.$\n",
    "\n",
    "但f'(xo)=0，所以上式即\n",
    "\n",
    "$\\frac{f'(x)}{x-x0}<0.$\n",
    "\n",
    "从而知道，对于这去心邻域内的x来说，f'(x）与x-x0符号相反．因此，当x-x0<0即x<x0时，f'(x)>0；当x-x0>0即x>x0时，f'(x)<0．于是根据定理2知道，f(x）在点x。处取得极大值．\n",
    "\n",
    "类似地可以证明情形（2).\n",
    "\n",
    "定理3表明，如果函数f(x）在驻点x处的二阶导数f\"(x0)≠0，那么该驻点x。一定是极值点，并且可以按二阶导数f\"(x0）的符号来判定f(x0）是极大值还是极小值．但如果f\"(x0)=0，那么定理3就不能应用．事实上，当f'(x0)=0,f\"(x0)=0时，f(x）在x0处可能有极大值，也可能有极小值，也可能没有极值．例如，$f1(x)=-x^4$,$f2(x)=x^4$,$f3(x)=x^2$这三个函数在x=0处就分别属于这三种情况．因此，如果函数在驻点处的二阶导数为零，那么可以用一阶导数在驻点左右邻近的符号来判定；如果函数在驻点处有$f\"(x0)=…=f^(n-1)(x0)=0$,$f^(n)(x0)≠0$，那么也可利用具有佩亚诺余项的泰勒公式来讨论判定（参阅本节习题4).\n",
    "例2 求函数$f(x)=(x^2-1)^3+1$的极值．\n",
    "\n",
    "解 $f'(x)=6x(x^2-1)^2$.\n",
    "\n",
    "令f'(x)=0，求得驻点x1=-1,x2=0,x3=1.\n",
    "\n",
    "$f\"(x)=6(x^2-1)(5x^2-1)$.\n",
    "\n",
    "因f\"(0)=6>0，故f(x）在x=0处取得极小值，极小值为f(0)=0.\n",
    "\n",
    "因f\"(-1)=f\"(1)=0，故用定理3无法判别．考察一阶导数f'(x）在驻点x1=-1及x3=1左右邻近的符号：\n",
    "\n",
    "当x取﹣1左侧邻近的值时，f'(x)<0；当x 取﹣1右侧邻近的值时，f'(x)<0；因为f'(x）的符号没有改变，所以f(x）在x=-1处没有极值．同理，f(x）在x=1处也没有极值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义函数\n",
    "def f(x):\n",
    "    return (x**2 - 1)**3 + 1\n",
    "\n",
    "# 生成x值\n",
    "x = np.linspace(-1.5, 1.5, 400)  # 在-1.5到1.5之间生成400个等间距的点\n",
    "\n",
    "# 计算y值\n",
    "y = f(x)\n",
    "\n",
    "# 绘制图像\n",
    "plt.plot(x, y, label=r'$f(x) = (x^2 - 1)^3 + 1$')\n",
    "\n",
    "# 添加标题和标签\n",
    "plt.title('Plot of the Function $f(x) = (x^2 - 1)^3 + 1$')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "\n",
    "# 显示图例\n",
    "plt.legend()\n",
    "\n",
    "# 显示网格\n",
    "plt.grid(True)\n",
    "\n",
    "# 显示图像\n",
    "plt.show()"
   ]
  }
 ],
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